Question: Reduce to lowest terms: $- \dfrac{7}{2} \div - \dfrac{9}{8} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{9}{8}$ is $- \dfrac{8}{9}$ Therefore: $ - \dfrac{7}{2} \div - \dfrac{9}{8} = - \dfrac{7}{2} \times - \dfrac{8}{9} $ $ \phantom{- \dfrac{7}{2} \times - \dfrac{8}{9}} = \dfrac{-7 \times -8}{2 \times 9} $ $ \phantom{- \dfrac{7}{2} \times - \dfrac{8}{9}} = \dfrac{56}{18} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{56}{18} = \dfrac{56 \div 2}{18 \div 2} = \dfrac{28}{9} $